Question

if 2x^3-ax^2-5x+6 is exactly divisible by x-3, then the polynomial is​

Answer 1

If the polynomial is divisible by x - 3, then the polynomial is the factor of another polynomial.

Answer 2

Answer:

see below :

Step-by-step explanation:

Let the given polynomial be p(x)=x

3

+ax

2

+bx+6

Given p(x) is divisible by (x–2), hence p(2)=0

Put x=2 in p(x)

p(2)=2

3

+a(2)

2

+b(2)+6

⇒0=8+4a+2b+6

⇒4a+2b=–14

⇒2a+b=–7 (1)

It is also given that when p(x) is divided by (x–3) the remainder is 3

That p(3)=3

Put x=3 in p(x)

p(3)=3

3

+a(3)

2

+b(3)+6

⇒3=27+9a+3b+6

⇒9a+3b=–30

⇒3a+b=–10 (2)

Subtract (2) from (1)

2a+b=–7

3a+b=–10

-------------------

–a=3

∴a=–3

Substitute a=–3 in (1), we get

2(–3)+b=–7

∴b=–1

b

a

=

−1

−3

=3